Applied noncentral Chi-squared distribution in CFAR detection of hyperspectral projected images

Abstract

In this paper, the noncentral chi-squared distribution is applied in the Constant False Alarm Rate (CFAR) detection of hyperspectral projected images to distinguish the anomaly points from background. Usually, the process of the hyperspectral anomaly detectors can be considered as a linear projection. These operators are linear transforms and their results are quadratic form which comes from the transform of spectral vector. In general, chi-squared distribution could be the proper choice to describe the statistical characteristic of this projected image. However, because of the strong correlation among the bands, the standard central chi-squared distribution often cannot fit the stochastic characteristic of the projected images precisely. In this paper, we use a noncentral chi-squared distribution to approximate the projected image of subspace based anomaly detectors. Firstly, the statistical modal of the projected multivariate data is analysed, and a noncentral chi-squared distribution is deduced. Then, the approach of the parameters calculation is introduced. At last, the aerial hyperspectral images are used to verify the effectiveness of the proposed method in tightly modeling the projected image statistic distribution.